Magnitude - Measuring Brightness

Mike Swanson

More than two thousand years ago, the first recorded attempt to quantify the brightness of sky objects was undertaken by the Greek astronomer Hipparcos.  His scale of measurement varied from first to sixth magnitude.  First magnitude stars were the brightest he could see, while sixth magnitude were the faintest.  As the science of astronomy progressed, the magnitude system was refined to allow precise measurements of all celestial objects.  For example, Venus is brighter than the brightest star and reaches a magnitude of more than -4 at times.  The brightest star in the sky, Sirius, is magnitude -1.  From a dark, clear site, the faintest stars most can see are magnitude 6, just as Hipparcos designated.  The following chart estimates the magnitude limits visible in various sized instruments under dark skies.

Instrument

Aperture

Limiting Magnitude

Naked eye

About 7mm

6

Binoculars

50mm

9.5

Telescopes:

 

 

 

60 mm (2.4 in.)

10.5

 

80 mm (3.1 in.)

11.3

 

4 in.

11.7

 

114 mm (4.5 in)

12

 

5 in.

12.3

 

8 in.

13.3

 

11 in.

14

 

14 in.

14.6

A difference of 1 in magnitude is actually a difference of 2 1/2 in brightness.  Thus, the difference in brightness between a magnitude 2 star and a magnitude 4 star is 6.25 - 2 1/2 times 2 1/2.  This explains why larger and larger instruments only gain fractional improvements in limiting magnitude.  Nonetheless, these fractional differences are significant.  The relatively modest step of just 1 magnitude difference between a 5 inch and 8 inch telescope brings many thousands of faint deep sky objects into view.

We can estimate the magnitude of naked eye objects using a couple of the most recognizable star formations in the sky.  For viewers in the Northern Hemisphere, turn to the Little Dipper.  In the Southern Hemisphere, refer to the Southern Cross.  The magnitudes of their various stars are shown in this figure:

 

Magnitude figures for deep sky objects are not as clear-cut as those for stars and planets.  Generally the entire luminosity of the object is “summed up” and reported as if it were a single point light source (a star).  So, a very large object of several arcminutes could be reported with a fairly bright magnitude, but appear very faint in the eyepiece.  This is typically the case for nebulae and galaxies.  Consider the Andromeda Galaxy, M31.  It is generally reported as approximately magnitude 3.4, but that 3.4 is spread out in an area of about 180 by 60 arcminutes.  This is about 6 times the width of the full moon!  So, while a star of magnitude 3.4 is easily visible to the naked eye, M31 requires dark clear skies to be glimpsed without optical aid.

In the case of deep sky objects, a better measure of luminosity is "surface brightness".  Surface brightness is not standardized and thus varies from one recorder to another, but is generally a measurement of magnitude per square arcsecond.  Thus we can better compare deep sky objects and determine whether we should be able to view them in our telescope or binoculars.  One slight complication for using surface brightness is the fact that not all objects are uniformly bright across their entire surface.  Again consider M31.  The core is many times brighter than the surrounding spiral arms.  Thus, the surface brightness of the core is higher than the average surface brightness of the entire galaxy.


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